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Game theory and hangman.
August 19, 2010 9:26 AM   Subscribe

'Jazz' is the best word to use in hangman.
posted by shakespeherian (96 comments total) 22 users marked this as a favorite

But this is on the internet, and computers are the internet, so YOU GAVE AWAY THE SECRET! Computers will never lose again!
posted by filthy light thief at 9:29 AM on August 19, 2010


etaoinshrdlu.

I win.
posted by Herodios at 9:31 AM on August 19, 2010


After reading Stephen Wolfram's interview about his setup, I'm convinuced that the reason that I find Wolfram|Alpha useless is that it wasn't made for me. It was made for Stephen Wolfram.
posted by The Devil Tesla at 9:34 AM on August 19, 2010 [13 favorites]


All this fucking around and Mathematica still doesn't have a proper Undo command.
posted by Wolfdog at 9:35 AM on August 19, 2010 [6 favorites]


Is this something you'd have to understand to understand?
posted by spicynuts at 9:40 AM on August 19, 2010 [25 favorites]


etaoinshrdlu.

I win.

Except there's neither a j nor a z in those letters and you've just lost any game with 11 or fewer wrong guesses allowed. You've actually illustrated the effectiveness of the word 'jazz' against a naïve letter frequency algorithm.

I did find it odd that in his version of the game the first few wrong guesses result in the drawing of the gallows itself. In every version of the game I've seen or played, the gallows is drawn at the outset and only the parts of the man are drawn as a result of wrong guesses. So a typical game would end at the 6th wrong guess (head, body, 2 arms, 2 legs). If you were feeling charitable you would allow for hands and feet. If you were playing to lose you'd allow for fingers and toes.
posted by jedicus at 9:41 AM on August 19, 2010 [3 favorites]


I always liked using "Egypt".
posted by Solon and Thanks at 9:41 AM on August 19, 2010 [2 favorites]


"I'd like to answer, Pat. Is it, 'Skyjacking sleeveless beekeepers?'"
posted by Wolfdog at 9:43 AM on August 19, 2010 [6 favorites]


There are various designs of gallows and man; I learned on the one above, which has 13 elements, but I have seen many possibilities between 10 and 13, and there are probably others. I’ll call these the 10-game and 13-game. My design, the 13-game, is easier for the guesser, as he or she is allowed more mistakes before losing.

So you can guess half the alphabet? more like LAMEman. I draw the gallows ahead of time and you get head, body, arm, arm, leg, leg, DEAD.
posted by DU at 9:44 AM on August 19, 2010


X-ray, without the dash.
posted by P.o.B. at 9:45 AM on August 19, 2010


'Jazz' is the best word to use in hangman.

I don't believe the article says anything of the sort. At best, it says that "jazz" is the best word to use against a simplistic first-order approximation of the ideal strategy. Key bit from the article:
Of course, this is only one more step toward the Nash equilibrium point. If the guesser updates the algorithm to take into account that strategy, we will have to repeat this entire experiment, to get an even better strategy. Eventually the two algorithms would likely converge on a point where every word has the same win ratio, and we will know the optimal game outcome.
(Important caveat: "every word has the same win ratio" is not the same as "every word is equally likely.")

The game-theoretic best strategy is a probabilistic distribution of words that minimizes the likelihood of the guesser winning, even if the guesser knows your probabilistic distribution of words. It's possible that the ideal probability distribution does have "jazz" as the most likely word, but even then I imagine its probability is quite low, just slightly larger than many other words.
posted by DevilsAdvocate at 9:45 AM on August 19, 2010 [3 favorites]


Another awesome one, if you're doing place names, is Lome, Togo. Almost everyone thinks it's going to be Rome.
posted by reenum at 9:45 AM on August 19, 2010


OXYGEN is an excellent hangman word.
posted by jozxyqk at 9:46 AM on August 19, 2010


Wait, the Nash Equilibrium can help you win at hangman and get you a date of medium attractiveness? Is there anything it doesn't do?
posted by Riki tiki at 9:46 AM on August 19, 2010 [3 favorites]


LYNX is a good hangman word, too.
posted by thescientificmethhead at 9:50 AM on August 19, 2010


etaoinshrdlu.

I win.

Except there's neither a j nor a z in those letters

My opponent can only use "jazz" once.

When you play craps, do you only roll the dice once?

I plug in etaoinshrdlu every time -- modified by my knowledge of English orthography -- and over time I win most of the plays.
posted by Herodios at 9:54 AM on August 19, 2010


My favorite word for hangman is chamois.
posted by shakespeherian at 9:55 AM on August 19, 2010


GYPSY is another excellent word for Hangman.

Of course, the danger of using a word with "y" as its only vowel is that people have the tendency to pitch fits after incorrectly guessing the first five vowels. Put a damper on my grade school days.
posted by estlin at 9:56 AM on August 19, 2010


OK, let's try it out: 
|----|
|    0
|   -|-
|   / \
|
-------

_ _ _ _

posted by stavrogin at 9:57 AM on August 19, 2010 [5 favorites]


Um, A?
posted by jontyjago at 10:00 AM on August 19, 2010 [2 favorites]


dammit.

_ A _ _
posted by stavrogin at 10:00 AM on August 19, 2010 [17 favorites]


My opponent can only use "jazz" once.

Maybe, but there are a lot more words that beat your approach (for the 10-game): buzz, hajj, fizz, fizzy, fuzz, fuzzy, puff, puffy, and buff, for example. There are no doubt many more. The weighted-frequency approach that the guessing algorithm described in the article uses is a substantial improvement over a straight etaoinshrdlu approach.
posted by jedicus at 10:00 AM on August 19, 2010


ETAOIN SHRDLU would be an awesome metal band name.
posted by nonreflectiveobject at 10:01 AM on August 19, 2010


Dude. Awesome hangman art.
posted by stoneweaver at 10:02 AM on August 19, 2010


LYNX is a good hangman word, too.

I don't agree.

I usually begin with the vowels, at least until I get a sense that there are "enough" vowels filled in for the length of the word. So for this, I would go E, A, I, O, U—five misses.

But having none of the standard five vowels makes Y a virtual certainty, so I guess Y, and get -Y--.

There's a very small number of words matching this pattern. Assuming we're not getting into really obscure words or proper names, we're left with cyst, hymn, lynx, myth, or sync. You can discriminate between those five possibilities with at most one more miss.
posted by DevilsAdvocate at 10:02 AM on August 19, 2010


I agree with all those who think 10-13 wrong guesses is entirely too high. I mean, I guess he's playing with his young kid, so that would be factored in. But generally, I can guess any word with 13 guesses.
posted by muddgirl at 10:02 AM on August 19, 2010


I still think the best hangman word is "help."

What - you don't agree? Fine, let's try it. Here, I have a noose; just step this way for a moment...
posted by koeselitz at 10:03 AM on August 19, 2010 [5 favorites]


There is no way that "Jazz" beats my battle tested champion "Syzygy".
posted by Freen at 10:05 AM on August 19, 2010 [6 favorites]


I still think the best hangman word is "help."

What - you don't agree? Fine, let's try it. Here, I have a noose; just step this way for a moment...

I think we were talking best word, not safeword.
posted by Herodios at 10:05 AM on August 19, 2010 [2 favorites]


Probe is a pretty good game. If you see it at the thrift store or garage sale or whatever, you ought to pick it up.
posted by box at 10:06 AM on August 19, 2010 [1 favorite]


Of course, the danger of using a word with "y" as its only vowel is that people have the tendency to pitch fits after incorrectly guessing the first five vowels.

Or, they know enough to guess Y next. -Y--Y with no other vowels? Really, how many possibilities are there?
posted by DevilsAdvocate at 10:08 AM on August 19, 2010


ETAOIN SHRDLU would be an awesome metal band name.

It's been done.
posted by Herodios at 10:09 AM on August 19, 2010 [1 favorite]


One of the best words for what I will call the traditional game (i.e., dead on 6 guesses, none of this 10 or 13 nonsense) is probably cwm. Guessing all of the vowels plus y is actually a losing strategy against that word. And even though it's a 3 letter word you still have to guess y because the word might be cry, for example.

-Y--Y with no other vowels? Really, how many possibilities are there?

The Scrabble dictionary says byway dykey gypsy myopy pygmy and typey. Those are variable enough to give you trouble.
posted by jedicus at 10:12 AM on August 19, 2010 [1 favorite]


Oh, whoops. Missed the whole 'no other vowels' part. So...gypsy and pygmy, then. Yeah, guess 'g' next and you have it.
posted by jedicus at 10:13 AM on August 19, 2010


We played a lot of hangman during my calculus class in high school. One day, these two guys were playing, and the person guessing guessed all 26 letters. None of them were in the word. At this point the person who was thinking of the word burst into oddly maniacal laughter and shouted, "You thought I was thinking of a word, but actually I was thinking of a picture of an octopus!" Then he drew a picture of an octopus where the word was supposed to go and sat down. In my mind, this is THE winning hangman strategy.
posted by martinX's bellbottoms at 10:14 AM on August 19, 2010 [38 favorites]


And "condominium" is the best word to use in Charades. And not because it's difficult, either.
posted by Decani at 10:18 AM on August 19, 2010


Ugg, this is the link that I meant to put up here.
posted by The Devil Tesla at 10:19 AM on August 19, 2010


My favorite hangman word is "moist". Just because.
posted by inigo2 at 10:22 AM on August 19, 2010 [1 favorite]


No Ytterbium?
posted by benzenedream at 10:22 AM on August 19, 2010


My 1985 AHD contains, somewhere between 'tenacious' and 'tentative' the item '1080' (sodium fluoroacetate, an ingredient in rat poison). It passes the 'in the dictionary' test -- as does 'nth' -- if you bring the right dictionary.
posted by Herodios at 10:27 AM on August 19, 2010


I got punched once for "mxyzptlk".
posted by jenkinsEar at 10:28 AM on August 19, 2010 [4 favorites]


the person guessing guessed all 26 letters. None of them were in the word.

That must have been an elaborate gallows setup.
posted by Gator at 10:28 AM on August 19, 2010


I got punched once for "mxyzptlk".

Well, Scrabble now permits proper names.
posted by Herodios at 10:31 AM on August 19, 2010


We played a lot of hangman during my calculus class in high school. One day, these two guys were playing, and the person guessing guessed all 26 letters. None of them were in the word. At this point the person who was thinking of the word burst into oddly maniacal laughter and shouted, "You thought I was thinking of a word, but actually I was thinking of a picture of an octopus!" Then he drew a picture of an octopus where the word was supposed to go and sat down. In my mind, this is THE winning hangman strategy.

In a math class, you'd think he could be a lot more creative than that. How about π or א 0 or just 5?
posted by kmz at 10:32 AM on August 19, 2010 [1 favorite]


Well, Scrabble now permits proper names.

No, it doesn't.
posted by lumensimus at 10:36 AM on August 19, 2010 [3 favorites]


My first wife used to stump me with "kayak".
posted by Araucaria at 10:42 AM on August 19, 2010


Except there's neither a j nor a z in those letters and you've just lost any game with 11 or fewer wrong guesses allowed. You've actually illustrated the effectiveness of the word 'jazz' against a naïve letter frequency algorithm.

OK, then, how about this one:
J    Z Z
Hint 1: Often hot, like jazz, but rarely cool, like jazz.
posted by Civil_Disobedient at 10:43 AM on August 19, 2010 [4 favorites]


Juzz?
posted by aramaic at 10:51 AM on August 19, 2010


Jwzz?
posted by box at 10:52 AM on August 19, 2010


Jizz?
posted by stavrogin at 10:53 AM on August 19, 2010


J[octopus drawing]zz?
posted by shakespeherian at 10:53 AM on August 19, 2010 [15 favorites]


Jay-Z?
posted by box at 10:55 AM on August 19, 2010 [1 favorite]


Augh. That article is maddening to read, because he barely labeled any of his graphs.
posted by schmod at 10:55 AM on August 19, 2010


Dammit, Freen, you beat me to "syzygy". It's my sekrit weapon!

Someone mentioned "statistical frequency" above. I have found that short words are way better than long words. That's why "jazz" is so good. It only has three letters, one of which is a "z". A word like "bit" might be good, but "t" is one of the 5 most common consonants (t,n,r,l,s).

I bet "bocce" would start some fights.
posted by Xoebe at 10:58 AM on August 19, 2010


One of the best words for what I will call the traditional game (i.e., dead on 6 guesses, none of this 10 or 13 nonsense) is probably cwm. Guessing all of the vowels plus y is actually a losing strategy against that word.

It would be interesting to try to come up with the shortest possible list of words for which there is not a guaranteed win for the guesser in the 6-game, where the guesser knows the list of words in advance.
posted by DevilsAdvocate at 11:05 AM on August 19, 2010 [2 favorites]


When I was in elementary school I could always stump my fellow hangman players by using "yacht" as my word.
posted by Oriole Adams at 11:19 AM on August 19, 2010


"syzygy" is actually pretty easy to get in six guesses -- assuming the strategy that starts by guessing vowels until you get at least one of them -- because it's probably the only word of the form ?y?y?y. And as has been pointed out, you really would want to mix things up and not play the "extreme" words all the time.

(I'm teaching game theory this semester, so I'm going to see if I can work this into my class. Have kids these days played hangman?)
posted by madcaptenor at 11:27 AM on August 19, 2010 [2 favorites]


It would be interesting to try to come up with the shortest possible list of words for which there is not a guaranteed win for the guesser in the 6-game, where the guesser knows the list of words in advance.

Oooh, I think I've got it, and the list is shorter than I had expected. Once I had the necessary flash of insight, it wasn't too hard to go about it. I'm pretty sure there's no guaranteed winning strategy for the guesser in the 6-game against a word selected from this list (there may be a slightly smaller subset of this list which would also work; I haven't rigorously checked for that yet):

BIB BOB BUB DAD DID DUD GAG GIG MOM MUM PAP PIP POP PUP TAT TIT TOT TUT

Or as an aid to analysis: 
  B D G M P T
A   * *   * *
I * * *   * *
O *     * * *
U * *   * * *

posted by DevilsAdvocate at 11:32 AM on August 19, 2010 [2 favorites]


I've always found "Kentucky" to be more devilish than it appears.
posted by Navelgazer at 11:32 AM on August 19, 2010


If you like incredibly challenging hangman I highly recommend Wits! For the iPhone and iPad. So far my absolute best is guessing the word in seven steps.

The twist? You guess an entire 5-letter Word, and are only told how many letters you have correct, and how many you have in the right word position, but not which letters are the correct ones. Fiendish.

I've found the best strategy for me is guessing words with duplicate letters, say PUPPY, and then switching a couple, HAPPY, and eliminating from there.
posted by misha at 11:35 AM on August 19, 2010


Crwth
posted by empath at 11:41 AM on August 19, 2010


No comment on the excessive Wolfram product plugs in the post? What interesting factoids: did you know John Nash uses Mathematica, there's usually a Mathematica user among the Nobel Prize winners, oh if only I could have used Wolfram|Alpha....
posted by JHarris at 11:52 AM on August 19, 2010 [1 favorite]


BIB BOB BUB DAD DID DUD GAG GIG MOM MUM PAP PIP POP PUP TAT TIT TOT TUT

I think DevilsAdvocate just wrote the lyrics for Lady Gaga's next single.
posted by Faint of Butt at 11:54 AM on August 19, 2010 [4 favorites]


You can get surprisingly far against human players just by using a lot of U's. A lot of people start by guessing the vowels, and U is the least common of the lot, so you force them to throw a way a few turns right at the beginning. You'll do even better against etaoinshrdluists. And it seems like if someone's having a hard time in hangman and they get a U, they'll throw away another turn by guessing Q next, which feels clever but isn't a very sound move for them at all.

On the other hand, something like _U_U isn't a statistical dead giveaway like _Y__Y is. GURU? KUDU? KURU? FUGU? MUMU? TUTU? There's enough possibilities to keep even a serious crossword geek stumped for a while, even after they've got the vowels filled in.

WHY YES I DO LIKE BEANS I WONDER WHY THAT IS?
posted by nebulawindphone at 11:56 AM on August 19, 2010 [1 favorite]


BIB BOB BUB DAD DID DUD GAG GIG MOM MUM PAP PIP POP PUP TAT TIT TOT TUT
[Bass:] BLUUUUUUUE...... MOON.
posted by nebulawindphone at 11:56 AM on August 19, 2010 [3 favorites]


... At this point the person who was thinking of the word burst into oddly maniacal laughter and shouted, "You thought I was thinking of a word, but actually I was thinking of a picture of an octopus!" ...

My wife won't play 20 questions with me any more. (I still think "Spreadsheet Software" is a perfectly good puzzle-object, dammit!)
posted by sebastienbailard at 11:58 AM on August 19, 2010


ETAOIN SHRDLU would be an awesome metal band name.

ËTÄÖÏN SHRDLÜ, you mean?
posted by maxwelton at 12:17 PM on August 19, 2010 [2 favorites]


jharris: it was written by a Wolfram employee on the Wolfram blog as a way of promoting Mathematica.
posted by empath at 12:42 PM on August 19, 2010


I didn't see "rhythm" on their list. Any hangman list that doesn't include rhythm doesn't count.
posted by rtimmel at 12:49 PM on August 19, 2010


On preview -- the "y" thing. Never mind.
posted by rtimmel at 12:50 PM on August 19, 2010


One of my favorite childhood "aha!" moments was when I realized that, no, choosing really long words for Hangman is actually not a good idea (even if it gives you an excuse to write 'antidisestablishmentarianism' on the blackboard).
posted by wanderingmind at 1:04 PM on August 19, 2010


I'm convinuced that the reason that I find Wolfram|Alpha useless is that it wasn't made for me. It was made for Stephen Wolfram.

Yup. Also, you're one click away from understanding every Apple product ever.
posted by rokusan at 1:12 PM on August 19, 2010


The Scrabble dictionary says byway dykey gypsy myopy pygmy and typey. Those are variable enough to give you trouble.

As a bonus, a couple of those could even start a bar fight, depending on your company.
posted by rokusan at 1:14 PM on August 19, 2010 [2 favorites]


Well, it was. Way to ruin yet another thing, scientists.
posted by Eideteker at 1:16 PM on August 19, 2010


J _ Z Z
Hint 1: Often hot, like jazz, but rarely cool, like jazz.

Aww, you got cwm all over my hangman....
posted by chavenet at 1:20 PM on August 19, 2010 [1 favorite]


I call foul. By his algorithm, how can lax be more difficult than zax?

I've pondered this question before and against an intelligent player the most difficult words are the three letter words. (When I play, words of four letters and less are banned.)

An intelligent player knows there is one of two strategies to follow. The standard one is use the most common letters. If you know the Scrabble frequencies, that will get you far (although the S is purposely limited in Scrabble). That's E, A, I, O, R, T, N, S, L, U, G, D, C, B, M, P, Y, H, F, W, V, K, J, X, Z, Q.

By this strategy, jazz almost immediately gives away its vowel. (1 miss for E)

_ A _ _

The guesser can leap beyond the remaining vowels and go after the common consonants. Once R, T, N, S, and L are chosen (now six total misses). Combinations of _AI_ are the next most likely (MAID, PAID, MAIM), so "I" should be chosen. (now seven total misses)

You have by now really limited the remaining word possibilities.

Some words may still involve other vowels (DAUB, BAUD for U, DADO for O), but a more likely set would be those with third and fourth consonants. If it is not a double consonant, then you go with M (DAMP, CAMP, VAMP) and Y (BABY, GAMY, HAZY). (now nine misses). The remaining choice is double consonants and for _ A _ _, that means F (GAFF, DAFF) and Z. Once Z is chosen the answer is obvious.

This takes 11 turns, but a good player sniffs out that this is a word with unlikely letters (I would after M: jazz is more likely than GAMY for an opponent to choose.)

By this strategy the hardest word would be HUH.

A side note. By the standards of the frequency of letters in English Scrabble, the most unlikely natural (no blanks) seven letter word is JUMBUCK or UPCHUCK. If you include blanks to make up for extra Zs, then it's ZYZZYVA.
posted by dances_with_sneetches at 1:36 PM on August 19, 2010 [1 favorite]


My daughter once thought she'd stumped me with XANADU but I was triumphant after seeing _A_A_U.
posted by vespabelle at 1:36 PM on August 19, 2010


"If it is not, then the chooser takes great pleasure in drawing a component of a gallows with a man hanging from it."

My sister and I played with the gallows already drawn. It was just the body that was part of the game. Of course, besides all the appendages includeded here, we would do feet, hands, two eyes, a nose, and a mouth. I wonder why the asker never won?

Anyway, how did youse guyses play - gallows already drawn, or drawn as part of the game?
posted by mreleganza at 1:37 PM on August 19, 2010


I like to choose the Quick Brown Fox Jumps Over the Lazy Dog as my hangman "word" because I am particularly fond of the plays of Samuel Beckett
posted by I Foody at 1:40 PM on August 19, 2010


I don't see the point of pre-drawing the gallows. Seems like extra work for no reason.

I generally play to ten points. (Four strokes of the pen for the gallows and six for its luckless victim.) I may get into drawing things like fingers and facial features if I'm playing against a little kid who needs more guesses, but I always start with a blank piece of paper.

Can anybody who pre-draws the gallows explain why?
posted by the latin mouse at 2:07 PM on August 19, 2010


Latin Mouse, I don't know if I could explain it some "a-ha!" kind of way, it's just the way we've always done it. I supposed to provides a bit of context....you probably could play tic-tac-toe fairly easily without a grid, but you still draw it. Not the perfect comparison but the first one to come to mind.
posted by mreleganza at 2:17 PM on August 19, 2010


I've always used ZEPHYR as my go-to hangman word.

And yeah, always played with the scaffolding already drawn. Head, body, arm, arm, leg, leg, eyes, nose, mouth (preferably twisted in a rictus of terror, cause, ya know dude's being hanged)

9 guesses.
posted by rbellon at 2:40 PM on August 19, 2010


Drawing in the gallows is just how I learned to play. In a boring meeting, a gallows and some dashes is a good way to signal, "Let's pass the time with some hangman." Otherwise they may think you just drew some dashes.
posted by muddgirl at 2:42 PM on August 19, 2010 [1 favorite]


One time in a game of movie-title Hangman I used π and barely escaped with my life.
posted by valrus at 2:51 PM on August 19, 2010 [2 favorites]


Similar to my earlier list, I believe I've found a surprisingly short (though probably not minimal) list of four-letter words against which there is no guaranteed win in the 6-game:

CAKE CANE CARE CAVE COKE CONE CORE COVE DALE DARE DOLE DONE DOVE HALE HARE HAVE HOLE HONE MAKE MALE MANE MARE MOLE MORE MOVE WAKE WALE WANE WARE WAVE WOKE WORE WOVE

a.k.a. my "Have an 'E', it won't help" list. The general form is [CDHMW][AO][KLNRV]E.

Also I've come up with a list of 115 fairly common four-letter words matching [BCDFGHJMW][AIOY][KLNPRSTVZ]E for which I suspect there is no guaranteed winning strategy even in the 10-game, though I haven't actually done the analysis.
posted by DevilsAdvocate at 2:59 PM on August 19, 2010 [2 favorites]


xerox has always been mine
posted by PinkMoose at 3:13 PM on August 19, 2010


"J _ Z Z
Hint 1: Often hot, like jazz, but rarely cool, like jazz."

Hmmm... Is it jazz?
posted by I-baLL at 3:18 PM on August 19, 2010


I have never lost using "quiz."
posted by danb at 4:01 PM on August 19, 2010


Is it Ghostbusters 2?
posted by kittyprecious at 4:24 PM on August 19, 2010


Also I've come up with a list of 115 fairly common four-letter words matching [BCDFGHJMW][AIOUY][KLNPRSTVZ]E

FTFM.
posted by DevilsAdvocate at 6:59 PM on August 19, 2010


Vodka is a sure winner against a human, never tested it against a computer.
posted by JujuB at 7:29 PM on August 19, 2010


I once solved a Wheel of Fortune puzzle with no letters showing (and one wrong letter guessed):

----'-
------
(Phrase; no T)
posted by DevilsAdvocate at 7:47 PM on August 19, 2010


My favorite is "twelfth." It usually hangs 'em.
posted by bz at 8:56 PM on August 19, 2010


King's Ransom
posted by Galaxor Nebulon at 9:38 AM on August 20, 2010


Oooh, that would fit too, Galaxor; never thought of that one. But it wasn't the answer in this case.
posted by DevilsAdvocate at 9:55 AM on August 20, 2010


For anyone still reading, it was "Here's Johnny"
posted by DevilsAdvocate at 2:32 PM on August 27, 2010


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